ОДНОРОДНАЯ КРАЕВАЯ ЗАДАЧА РИМАНА С МЕРОМОРФНЫМИ КОЭФФИЦИЕНТАМИ ДЛЯ БЕСКОНЕЧНО СВЯЗНЫХ ОБЛАСТЕЙ

Homogeneous Riemann boundary value problem with meromorphic coefficients for infinitely connected domains is considered. In the closed form the problem is solved in the class of piece-wise analytic functions, possessing meromorphic continuation to the whole complex plane. Special attention is paid to the existence of doubly periodic solutions to the problem with elliptic coefficients. The example of the problem having a unique solution up to an arbitrary constant multiplier is presented, as well as of the problem with a solution depending on a number of arbitrary parameters. The obtained results can be used for solving of an inhomogeneous Riemann boundary value problem with meromorphic coefficients in an infinitely connected domain in the general statement.В исследованиях эффективных свойств двумерных композиционных материалов наиболее изученным является случай материалов с периодической микроструктурой. Это связано с возможностью представления решений соответствующих краевых задач через значения некоторых эллиптических функций. В данной работе рассматривается однородная краевая задача Римана для бесконечно связных областей и мероморфных коэффициентов. В замкнутой форме дается решение задачи в классе кусочно-аналитических функций, допускающих мероморфное продолжение на всю комплексную плоскость. Как частный случай решается вопрос существования и единственности двоякопериодических решений задачи с эллиптическим коэффициентом. Приводится пример задачи, имеющей единственное, с точностью до произвольного числового множителя, решение, и пример задачи, решение которой зависит от произвольных независимых параметров. Полученные результаты могут служить базой для исследования случая, когда коэффициенты задачи являются различными для каждого из контуров, а также при решении неоднородной задачи Римана с мероморфными коэффициентами и свободными членами в бесконечно связных областях.

Nonlinear excitation of kinetic Alfven waves and whistler waves by electron beam-driven Langmuir waves in the solar corona

© ESO 2003We study a new nonlinear excitation mechanism of kinetic Alfvén waves (KAWs) and whistler waves (Ws) by electron beam-driven Langmuir waves (Ls). The generation conditions for the parametric decay instability L W + KAW are determined and the growth rate is calculated. We show that the resonant pairs of KAWs and whistler waves are nonlinearly coupled to the pump Langmuir waves and their amplitudes undergo exponential growth from the thermal level. The perpendicular dispersion of KAWs strongly increases the coupling due to the nonlinear current parallel to the ambient magnetic field. Our study suggests that the nonlinear coupling of Langmuir wave energy into KAWs and whistlers can provide an efficient sink for weakly dispersive Langmuir waves excited by fast electron beams in the solar corona when the electron plasma frequency is lower than the electron gyrofrequency. This condition can be satisfied in the low-density magnetic filaments that are rooted in the depleted patches at the coronal base and extend to the high corona. At the same time, the Langmuir-driven KAWs and whistlers give rise to scattering and/or thin structures of radio emission penetrating through, or generated in these regions. Since the decay into sunward propagating KAWs is strongest, the nonlinearly driven KAWs can be easily distinguished from the waves generated at the coronal base and propagating away from the Sun. Our results may be used in the analysis of solar radio data and for remote probing of the coronal plasma, magnetic fields, and waves.Yu. Voitenko, M. Goossens, O. Sirenko and A. C.-L. Chia

Search for Primordial Black Holes with SGARFACE

The Short GAmma Ray Front Air Cherenkov Experiment (SGARFACE) uses the Whipple 10 m telescope to search for bursts of $\gamma$ rays. SGARFACE is sensitive to bursts with duration from a few ns to $\sim$20 $\mu$s and with $\gamma$-ray energy above 100 MeV. SGARFACE began operating in March 2003 and has collected 2.2 million events during an exposure time of 2267 hours. A search for bursts of $\gamma$ rays from explosions of primordial black holes (PBH) was carried out. A Hagedorn-type PBH explosion is predicted to be visible within 60 pc of Earth. Background events were caused by cosmic rays and by atmospheric phenomena and their rejection was accomplished to a large extent using the time-resolved images. No unambiguous detection of bursts of $\gamma$ rays could be made as the remaining background events mimic the expected shape and time development of bursts. Upper limits on the PBH explosion rate were derived from the SGARFACE data and are compared to previous and future experiments. We note that a future array of large wide-field air-Cherenkov telescopes equipped with a SGARFACE-like trigger would be able to operate background-free with a 20 to 30 times higher sensitivity for PBH explosions.Comment: 18 pages, 30 figures, accepted by Astroparticle Physics, corrected author list and Section 2.

Long term time variability of cosmic rays and possible relevance to the development of life on Earth

An analysis is made of the manner in which the cosmic ray intensity at Earth has varied over its existence and its possible relevance to both the origin and the evolution of life. Much of the analysis relates to the 'high energy' cosmic rays ($E>10^{14}eV;=0.1PeV$) and their variability due to the changing proximity of the solar system to supernova remnants which are generally believed to be responsible for most cosmic rays up to PeV energies. It is pointed out that, on a statistical basis, there will have been considerable variations in the likely 100 My between the Earth's biosphere reaching reasonable stability and the onset of very elementary life. Interestingly, there is the increasingly strong possibility that PeV cosmic rays are responsible for the initiation of terrestrial lightning strokes and the possibility arises of considerable increases in the frequency of lightnings and thereby the formation of some of the complex molecules which are the 'building blocks of life'. Attention is also given to the well known generation of the oxides of nitrogen by lightning strokes which are poisonous to animal life but helpful to plant growth; here, too, the violent swings of cosmic ray intensities may have had relevance to evolutionary changes. A particular variant of the cosmic ray acceleration model, put forward by us, predicts an increase in lightning rate in the past and this has been sought in Korean historical records. Finally, the time dependence of the overall cosmic ray intensity, which manifests itself mainly at sub-10 GeV energies, has been examined. The relevance of cosmic rays to the 'global electrical circuit' points to the importance of this concept.Comment: 18 pages, 5 figures, accepted by 'Surveys in Geophysics

Personalization as an approach to education

The article is devoted to the notion and role of personalization in teaching English as a tool of day-to-day and professional communication, considering modern methodology which heavily relies on Internet technologies. The authors analyze the development of the ideas, which have served as the basis for personalized education, and come up with a detailed inventory of popular models of personalized education both in Russia and abroad to check their adherence to basic principles of personalization. The methods used in the article comprise synchronic and diachronic forms of comparative analysis. The authors’ personal experience of teaching English in a personalized way at Skyeng School via its online platform has become an important extra source of empirical material for the article. The results of the undertaken study can be of practical value for administrators of educational organizations, specialists in teaching methodology, school teachers who would like to implement various methods of personalized education or devise a personalized technique on their ow

Meteor Trails and Columniform Sprites

A theoretical model of columniform sprites (or c-sprites), a distinctive class of high altitude, temporally brief optical emissions, is presented and compared to observations which extends earlier work (1998, E. M. D. Symbalisty, R. Roussel-Dupré, and V. Yukhimuk, EOS Transactions of the AGU 79, No. 45, p. F129) by making a strong connection with meteors. The key features of the model are: (1) an ambient conductivity profile that falls between a measured nighttime and a measured daytime conductivity; (2) an aerosol reduced conductivity in a trail from a meteor that passed through some time during the evening, and (3) a cloud-to-ground (hereafter CG) lightning stroke, with sufficient charge transfer, subsequent to and occurring within an hour of the development of the reduced conductivity trail. The model predicts a temporally brief column of light resulting from the conventional breakdown of air in a strong electric field in the observed altitude range. For the case of a positive CG stroke the emissions are extinguished by the passage of a runaway electron beam. The electron beam is initiated by the same positive CG lightning stroke that allows the high altitude conventional breakdown to occur and propagates from the cloud tops to the ionosphere. Based on our modeling results, a negative CG lightning stroke, for the same amount of charge transfer, produces a column of light about twice as bright. The emissions are extinguished, in this case, by the ambient conductivity taking into account the increase due to the conventional breakdown of air. In both cases, for the CG lightning stroke parameters examined here, the simulated c-sprite emissions are brief and last less than 17 ms, or one CCD video field

Integrative ecological and genetic monitoring of cloudberry (Rubus chamaemorus L.) populations on the southern border of the European and North American area (in Belarus and Minnesota)

The subjects of the study are the populations of Rubiis chamaemorus L. (cloudberry) in Belarus and the state of Minnesota (USA), where this circumpolar boreal species reaches the southern boundary of the distribution area and is protected by state (Minnesota) and national (Belarus) governments. There arc 17 known places of growth of R. chamaemorus in 14 administrative districts in Belarus and only 7 locations in Minnesota. In the context of global climate change, the study of such low-lalitude edge populations, which arc extremely important for the long-term survival and maintenance of the genetic diversity of the species, is particularly relevant as it helps to clarify the history and phylogeography of its distribution on the local landscape, and generally to assess the evolutionary potential of the species across its whole range [1]. The purpose and objectives of this study were to conduct integrated ecological and genetic studies: 1). to obtain quantitative and qualitative characteristics of the ecological parameters of habitat and the state of cloudberry populations in Belarus and Minnesota; 2). to develop an effective system for detecting variability of genomic DNA at the intra- and interpopulation levels using AFLP and SRAP markers aimed at identification of the genetic diversity (GD) parameters of populations.Объектом исследования являются популяции Rubus chamaemorus L. в Беларуси и Миннесоте (США), где этот циркумполярный дорсальный вид находиться на южной границе ареала распространения и охраняется законодательством штата (Миннесота) и Республики Беларусь. Такие «краевые» популяции являются наиболее уязвимыми к изменениям климата. Сравнительная оценка параметров эколого-ботанических особенностей среды их произрастания позволяет идентифицировать экологические предпочтения и лимитирующие факторы. Интегральный сравнительный анализ развития популяций, эколого-ботанических параметров среды, а также вариабельности генетического разнообразия позволит ответить на вопрос о происхождении популяций, оценить их подразделенность, адаптивный потенциал вида в исследуемых регионах, выявить аллели, расширяющие способность популяций противостоять и выдерживать резкие изменения качества среды. Проект направлен на получение новых данных по идентификации областей по сохранению вида, оптимизацию практических мер охраны его местообитаний и отдельных популяций

Integrative ecological and genetic monitoring of cloudberry (Rubus chamaemorus L.) populations on the southern border of the European and North American area (in Belarus and Minnesota)

The subjects of the study are the populations of Rubiis chamaemorus L. (cloudberry) in Belarus and the state of Minnesota (USA), where this circumpolar boreal species reaches the southern boundary of the distribution area and is protected by state (Minnesota) and national (Belarus) governments. There arc 17 known places of growth of R. chamaemorus in 14 administrative districts in Belarus and only 7 locations in Minnesota. In the context of global climate change, the study of such low-lalitude edge populations, which arc extremely important for the long-term survival and maintenance of the genetic diversity of the species, is particularly relevant as it helps to clarify the history and phylogeography of its distribution on the local landscape, and generally to assess the evolutionary potential of the species across its whole range [1]. The purpose and objectives of this study were to conduct integrated ecological and genetic studies: 1). to obtain quantitative and qualitative characteristics of the ecological parameters of habitat and the state of cloudberry populations in Belarus and Minnesota; 2). to develop an effective system for detecting variability of genomic DNA at the intra- and interpopulation levels using AFLP and SRAP markers aimed at identification of the genetic diversity (GD) parameters of populations.Объектом исследования являются популяции Rubus chamaemorus L. в Беларуси и Миннесоте (США), где этот циркумполярный дорсальный вид находиться на южной границе ареала распространения и охраняется законодательством штата (Миннесота) и Республики Беларусь. Такие «краевые» популяции являются наиболее уязвимыми к изменениям климата. Сравнительная оценка параметров эколого-ботанических особенностей среды их произрастания позволяет идентифицировать экологические предпочтения и лимитирующие факторы. Интегральный сравнительный анализ развития популяций, эколого-ботанических параметров среды, а также вариабельности генетического разнообразия позволит ответить на вопрос о происхождении популяций, оценить их подразделенность, адаптивный потенциал вида в исследуемых регионах, выявить аллели, расширяющие способность популяций противостоять и выдерживать резкие изменения качества среды. Проект направлен на получение новых данных по идентификации областей по сохранению вида, оптимизацию практических мер охраны его местообитаний и отдельных популяций